Table of Contents Author Guidelines Submit a Manuscript
Advances in High Energy Physics
Volume 2009, Article ID 905705, 9 pages
http://dx.doi.org/10.1155/2009/905705
Research Article

Thermodynamics in Loop Quantum Cosmology

Department of Physics, Beijing Normal University, Beijing 100875, China

Received 2 December 2008; Accepted 5 January 2009

Academic Editor: George Siopsis

Copyright © 2009 Li-Fang Li and Jian-Yang Zhu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Ashtekar and J. Lewandowski, “Background independent quantum gravity: a status report,” Classical and Quantum Gravity, vol. 21, no. 15, pp. R53–R152, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. L. Smolin, “An invitation to loop quantum gravity,” http://arxiv.org/abs/hep-th/0408048.
  3. C. Rovelli, “Loop quantum gravity,” Living Reviews in Relativity, vol. 1, pp. 1–68, 1998. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. C. Rovelli, Quantum Gravity, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, UK, 2004. View at Zentralblatt MATH · View at MathSciNet
  5. T. Thiemann, Modern Canonical Quantum General Relativity, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, UK, 2007. View at Zentralblatt MATH · View at MathSciNet
  6. M. Bojowald, “Absence of a singularity in loop quantum cosmology,” Physical Review Letters, vol. 86, no. 23, pp. 5227–5230, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  7. M. Bojowald, “Homogeneous loop quantum cosmology,” Classical and Quantum Gravity, vol. 20, no. 13, pp. 2595–2615, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. M. Bojowald and G. Date, “Quantum suppression of the generic chaotic behavior close to cosmological singularities,” Physical Review Letters, vol. 92, no. 7, Article ID 071302, 4 pages, 2004. View at Publisher · View at Google Scholar
  9. M. Bojowald, “The Bianchi IX model in loop quantum cosmology,” Classical and Quantum Gravity, vol. 21, no. 14, pp. 3541–3569, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. M. Bojowald, “Inflation from quantum geometry,” Physical Review Letters, vol. 89, no. 26, Article ID 261301, 4 pages, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  11. G. Date and G. M. Hossain, “Genericness of inflation in isotropic loop quantum cosmology,” Physical Review Letters, vol. 94, no. 1, Article ID 011301, 4 pages, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  12. H.-H. Xiong and J.-Y. Zhu, “Tachyon field in loop quantum cosmology: inflation and evolution picture,” Physical Review D, vol. 75, no. 8, Article ID 084023, 8 pages, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  13. S. W. Hawking, “Particle creation by black holes,” Communications in Mathematical Physics, vol. 43, no. 3, pp. 199–220, 1975. View at Publisher · View at Google Scholar · View at MathSciNet
  14. C. Rovelli, “Black hole entropy from loop quantum gravity,” Physical Review Letters, vol. 77, no. 16, pp. 3288–3291, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. A. Ghosh and P. Mitra, “Counting black hole microscopic states in loop quantum gravity,” Physical Review D, vol. 74, no. 6, Article ID 064026, 5 pages, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  16. A. Ashtekar, M. Bojowald, and J. Lewandowski, “Mathematical structure of loop quantum cosmology,” Advances in Theoretical and Mathematical Physics, vol. 7, no. 2, pp. 233–268, 2003. View at Google Scholar · View at MathSciNet
  17. G. W. Gibbons and S. W. Hawking, “Cosmological event horizons, thermodynamics, and particle creation,” Physical Review D, vol. 15, no. 10, pp. 2738–2751, 1977. View at Publisher · View at Google Scholar · View at MathSciNet
  18. R.-G. Cai and S. P. Kim, “First law of thermodynamics and Friedmann equations of Friedmann-Robertson-Walker universe,” The Journal of High Energy Physics, no. 2, article 050, pp. 1–13, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  19. M. Bojowald, “How quantum is the big bang?” Physical Review Letters, vol. 100, no. 22, Article ID 221301, 4 pages, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  20. C. W. Misner and D. H. Sharp, “Relativistic equations for adiabatic, spherically symmetric gravitational collapse,” vol. 136, pp. B571–B576, 1964. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. A. Ashtekar, T. Pawlowski, and P. Singh, “Quantum nature of the big bang: an analytical and numerical investigation,” Physical Review D, vol. 73, no. 12, Article ID 124038, 33 pages, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  22. A. Ashtekar, T. Pawlowski, and P. Singh, “Quantum nature of the big bang: improved dynamics,” Physical Review D, vol. 74, no. 8, Article ID 084003, 23 pages, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  23. J. Mielczarek, T. Stachowiak, and M. Szydlowski, “Exact solutions for a big bounce in loop quantum cosmology,” Physical Review D, vol. 77, no. 12, Article ID 123506, 13 pages, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  24. G. M. Hossain, “On energy conditions and stability in effective loop quantum cosmology,” Classical and Quantum Gravity, vol. 22, no. 13, pp. 2653–2670, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. K. Banerjee and G. Date, “Discreteness corrections to the effective Hamiltonian of isotropic loop quantum cosmology,” Classical and Quantum Gravity, vol. 22, no. 11, pp. 2017–2033, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. S. A. Hayward, “Unified first law of black-hole dynamics and relativistic thermodynamics,” Classical and Quantum Gravity, vol. 15, no. 10, pp. 3147–3162, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. M. Akbar and R. G. Cai, “Thermodynamic behavior of the Friedmann equation at the apparent horizon of the FRW universe,” Physical Review D, vol. 75, no. 8, Article ID 084003, 9 pages, 2007. View at Publisher · View at Google Scholar
  28. R.-G. Cai and L.-M. Cao, “Unified first law and the thermodynamics of the apparent horizon in the FRW universe,” Physical Review D, vol. 75, no. 6, Article ID 064008, 11 pages, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  29. S. A. Hayward, “Gravitational energy in spherical symmetry,” Physical Review D, vol. 53, no. 4, pp. 1938–1949, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  30. J. D. Brown and J. W. York Jr., “Quasilocal energy and conserved charges derived from the gravitational action,” Physical Review D, vol. 47, no. 4, pp. 1407–1419, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  31. C.-C. M. Liu and S.-T. Yau, “Positivity of quasilocal mass,” Physical Review Letters, vol. 90, no. 23, Article ID 231102, 4 pages, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  32. H.-H. Xiong and J.-Y. Zhu, “Violation of strong energy condition in effective loop quantum cosmology,” International Journal of Modern Physics A, vol. 22, no. 18, pp. 3137–3146, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet